Question 511 Mark
For what value of 'a' the vectors $\hat{\text{2i}}-\hat{\text{3j}}+\hat{\text{4k}}$ and $\hat{\text{ai}}-\hat{\text{6j}}-\hat{\text{8k}}$ are collinear?
Answer
View full question & answer→a = -4.
Questions · Page 2 of 3
1 Marks Question
Question 521 Mark
Write a vector of magnitude 15 units in the direction of vector.
Answer
View full question & answer→$5\hat{\text{i}}-10\hat{\text{j}}+10\hat{\text{k}}$.
Question 531 Mark
Write the vector equation of the following line: $\frac{\text{x-5}}{3}=\frac{\text{y+4}}{7}=\frac{\text{6-z}}{2}.$
Answer
View full question & answer→$\overrightarrow{\text{r}}=\Big(5\hat{\text{i}}-4\hat{\text{j}}+6\hat{\text{k}}\Big)+\lambda\ \Big(3\hat{\text{i}}+7\hat{\text{j}}-2\hat{\text{k}}\Big)$
Question 541 Mark
What is the cosine of the angle which the vector$\sqrt{2}\hat{\text{ i}}+\hat{\text{j}}+\hat{\text{k}}$ .
Answer
View full question & answer→$\frac{1}{2}$.
Question 551 Mark
Find the projection of a $\overrightarrow{a} \text{on} \overrightarrow{b} \text{if} \overrightarrow{a}. \overrightarrow{b} = 8$ and $\overrightarrow{b} = 2\hat{i} + 6\hat{j} + 3\hat{k}.$
Answer
View full question & answer→Given $\overrightarrow{a}. \overrightarrow{b} = 8$$\overrightarrow{b} = 2\hat{i} + 6\hat{j} + 3\hat{k}$
We know projection of $\overrightarrow{a}$ on $\overrightarrow{b}$ $= \frac{\overrightarrow{a}.\overrightarrow{b}}{|\overrightarrow{b}|}$
$= \frac{8}{\sqrt{4 + 36 + 9}} = \frac{8}{7}$
We know projection of $\overrightarrow{a}$ on $\overrightarrow{b}$ $= \frac{\overrightarrow{a}.\overrightarrow{b}}{|\overrightarrow{b}|}$
$= \frac{8}{\sqrt{4 + 36 + 9}} = \frac{8}{7}$
Question 561 Mark
Write the value of p for which $\overrightarrow{a} = 3\hat{i} + 2\hat{j} + 9\hat{k}$ and $\overrightarrow{b} = \hat{i} + \text{p}\hat{j} + 3\hat{k}$ are parallel vectors.
Answer
View full question & answer→Since $\overrightarrow{a} || \overrightarrow{b}$ therefore $\overrightarrow{a} = \lambda \overrightarrow{b}$$\Rightarrow (3\hat{i} + 2\hat{j} +9\hat{k} )=\lambda(\hat{i} + {p\hat{j} }+ 3\hat{k})$
$\Rightarrow \lambda = 3,\ 2 = \lambda p,\ 9 =3\lambda$
$\text{or} \lambda = 3, p = \frac{2}{3}$
$\Rightarrow \lambda = 3,\ 2 = \lambda p,\ 9 =3\lambda$
$\text{or} \lambda = 3, p = \frac{2}{3}$
Question 571 Mark
Write a unit vector in the direction of $\overrightarrow{a} = 2\hat{i} - 6\hat{j} + 3\hat{k}.$
Answer
View full question & answer→ $\frac{2}{7} \hat{i} - \frac{6}{7} \hat{j} + \frac{3}{7} \hat{k}$Unit vector in the direction $\overrightarrow{a} = \frac{\overrightarrow{a}}{|\overrightarrow{b}|} = \hat{a}$
$\Rightarrow \hat{a} = \frac{2\hat{i}- 6\hat{j} + 3\hat{k}}{\sqrt{4 + 36 + 9}}$
$\Rightarrow \hat{a} = \frac{2}{7} \hat{i} - \frac{6}{7} \hat{j} + \frac{3}{7} \hat{k}$
$\Rightarrow \hat{a} = \frac{2\hat{i}- 6\hat{j} + 3\hat{k}}{\sqrt{4 + 36 + 9}}$
$\Rightarrow \hat{a} = \frac{2}{7} \hat{i} - \frac{6}{7} \hat{j} + \frac{3}{7} \hat{k}$
Question 581 Mark
For what value of $\lambda$ are the vectors $\overrightarrow{a} = 2\hat{i} + \lambda\hat{j} + \hat{k}$ and $\overrightarrow{b} = \hat{i} - 2\hat{j} + 3\hat{k}$ prependicular to each other?
Answer
View full question & answer→ $\overrightarrow{a} \text{and} \overrightarrow{b}$ are prependicular if$\overrightarrow{a}.\overrightarrow{b} = 0$
$\Rightarrow(2\hat{i} + \lambda\hat{j} + \hat{k}) .( \hat{i} - 2\hat{j} + 3\hat{k}) = 0$
$\Rightarrow 2 - 2\lambda + 3 = 0 \Rightarrow \lambda= \frac{5}{2}.$
$\Rightarrow(2\hat{i} + \lambda\hat{j} + \hat{k}) .( \hat{i} - 2\hat{j} + 3\hat{k}) = 0$
$\Rightarrow 2 - 2\lambda + 3 = 0 \Rightarrow \lambda= \frac{5}{2}.$
Question 591 Mark
Find a unit vector in the direction of $\overrightarrow{a} = 3\hat{i} - 2\hat{j} + 6\hat{k}$
Answer
View full question & answer→$\overrightarrow{a} = 3\hat{i} - 2\hat{j} + 6\hat{k}$Unit vector in the direction of $\overrightarrow{a} = \frac{\overrightarrow{a}}{\overrightarrow{|a|}}$
$= \frac{3\hat{i} - 2\hat{j} + 6\hat{k}}{\sqrt{3^{2} +(-2)^{2}+ 6^{2}}} = \frac{1}{7}(3\hat{i} - 2\hat{j} + 6\hat{k})$
$= \frac{3\hat{i} - 2\hat{j} + 6\hat{k}}{\sqrt{3^{2} +(-2)^{2}+ 6^{2}}} = \frac{1}{7}(3\hat{i} - 2\hat{j} + 6\hat{k})$
Question 601 Mark
Find the angle between the vectors $\overrightarrow{a} = \hat{i} - \hat{j} +\hat{k}$ and $\overrightarrow{b} = \hat{i} + \hat{j} -\hat{k}$
Answer
View full question & answer→$\overrightarrow{a} = \hat{i} - \hat{j} +\hat{k} \Rightarrow \overrightarrow{|a|} = \sqrt{1^{2} + (-1)^{2} + 1^{2}} = \sqrt{3}$$\overrightarrow{b} = \hat{i} - \hat{j} +\hat{k} \Rightarrow \overrightarrow{|b|} = \sqrt{1^{2} + (1)^{2} + (-1)^{2}} = \sqrt{3}$
$\overrightarrow{a}.\overrightarrow{b} = \overrightarrow{|a|} \overrightarrow{|b|} \cos\Theta$
$\Rightarrow 1-1-1 = \sqrt{3}.\sqrt{3} \cos \theta \Rightarrow -1 = 3 \cos\theta$
$\Rightarrow \cos\theta = -\frac{1}{3} \Rightarrow \theta = \cos^{-1} \bigg(-\frac{1}{3}\bigg)$
$\overrightarrow{a}.\overrightarrow{b} = \overrightarrow{|a|} \overrightarrow{|b|} \cos\Theta$
$\Rightarrow 1-1-1 = \sqrt{3}.\sqrt{3} \cos \theta \Rightarrow -1 = 3 \cos\theta$
$\Rightarrow \cos\theta = -\frac{1}{3} \Rightarrow \theta = \cos^{-1} \bigg(-\frac{1}{3}\bigg)$
Question 611 Mark
Find the magnitude of each of the two vectors $\vec{\text{a}}\ \text{and}\ \vec{\text{b}},$ having the same magnitude such that the angle between them is 60° and their scalar product is $\frac{9}{2}.$
Answer
View full question & answer→Magnitude of two vectors $\vec{\text{a}}\ \&\ \vec{\text{b}}$ are same $|\vec{\text{a}}|=|\vec{\text{b}}|$
$\vec{\text{a}}\cdot\vec{\text{b}}=|\vec{\text{a}}||\vec{\text{b}}|\cos\theta$
$\frac{\text{a}}{2}=|\vec{\text{a}}||\vec{\text{a}}|\cos60^\circ$
$|\vec{\text{a}}|^2=\frac{9}{2}\times2=9$
$|\vec{\text{a}}|=3=|\vec{\text{b}}|$
$\vec{\text{a}}\cdot\vec{\text{b}}=|\vec{\text{a}}||\vec{\text{b}}|\cos\theta$
$\frac{\text{a}}{2}=|\vec{\text{a}}||\vec{\text{a}}|\cos60^\circ$
$|\vec{\text{a}}|^2=\frac{9}{2}\times2=9$
$|\vec{\text{a}}|=3=|\vec{\text{b}}|$
Question 621 Mark
Find the magnitude of each of the two vectors $\vec{\text{a}}\ \text{and}\ \vec{\text{b}},$ having the same magnitude such that the angle between them is 60° and their scalar product is $\frac{9}{2}.$
Answer
View full question & answer→Magnitude of two vectors $\vec{\text{a}}\ \&\ \vec{\text{b}}$ are same $|\vec{\text{a}}|=|\vec{\text{b}}|$
$\vec{\text{a}}\cdot\vec{\text{b}}=|\vec{\text{a}}||\vec{\text{b}}|\cos\theta$
$\frac{\text{a}}{2}=|\vec{\text{a}}||\vec{\text{a}}|\cos60^\circ$
$|\vec{\text{a}}|^2=\frac{9}{2}\times2=9$
$|\vec{\text{a}}|=3=|\vec{\text{b}}|$
$\vec{\text{a}}\cdot\vec{\text{b}}=|\vec{\text{a}}||\vec{\text{b}}|\cos\theta$
$\frac{\text{a}}{2}=|\vec{\text{a}}||\vec{\text{a}}|\cos60^\circ$
$|\vec{\text{a}}|^2=\frac{9}{2}\times2=9$
$|\vec{\text{a}}|=3=|\vec{\text{b}}|$
Question 631 Mark
Find the magnitude of each of the two vectors $\vec{\text{a}}\ \text{and}\ \vec{\text{b}},$ having the same magnitude such that the angle between them is 60° and their scalar product is $\frac{9}{2}.$
Answer
View full question & answer→Magnitude of two vectors $\vec{\text{a}}\ \&\ \vec{\text{b}}$ are same $|\vec{\text{a}}|=|\vec{\text{b}}|$
$\vec{\text{a}}\cdot\vec{\text{b}}=|\vec{\text{a}}||\vec{\text{b}}|\cos\theta$
$\frac{\text{a}}{2}=|\vec{\text{a}}||\vec{\text{a}}|\cos60^\circ$
$|\vec{\text{a}}|^2=\frac{9}{2}\times2=9$
$|\vec{\text{a}}|=3=|\vec{\text{b}}|$
$\vec{\text{a}}\cdot\vec{\text{b}}=|\vec{\text{a}}||\vec{\text{b}}|\cos\theta$
$\frac{\text{a}}{2}=|\vec{\text{a}}||\vec{\text{a}}|\cos60^\circ$
$|\vec{\text{a}}|^2=\frac{9}{2}\times2=9$
$|\vec{\text{a}}|=3=|\vec{\text{b}}|$
Question 641 Mark
Classify the following measures as scalar and vector:
10 meters south-east.
10 meters south-east.
Answer
View full question & answer→ 10 meters south-east is a vector quantity as it involve direction.
Question 651 Mark
If $\vec{\text{a}}$ ia a non-zero vector of modulus a and m is a non-zero scalar such that $\text{m}\vec{\text{a}}$ is the unit vector, write the value of m.
Answer
View full question & answer→ Given $\vec{\text{a}}$ is a non-zero vector of modulus a. Also, $\text{m}\vec{\text{a}}$ is the unit vector. Therefore,$|\text{m}\vec{\text{a}}|=1$
$\Rightarrow\ |\text{m}||\vec{\text{a}}|=1$
$\Rightarrow\ |\text{m}|\text{a}=1$
$\Rightarrow\ |\text{m}|=\frac{1}{\text{a}}$
$\Rightarrow\ \text{m}=\pm\frac{1}{\text{a}}$
$\Rightarrow\ |\text{m}||\vec{\text{a}}|=1$
$\Rightarrow\ |\text{m}|\text{a}=1$
$\Rightarrow\ |\text{m}|=\frac{1}{\text{a}}$
$\Rightarrow\ \text{m}=\pm\frac{1}{\text{a}}$
Question 661 Mark
Classify the following as scalar and vector quantities:
Acceleration.
Acceleration.
Answer
View full question & answer→ Acceleration is a vector quantity because it involves both magnitude as well as direction.
Question 671 Mark
Classify the following as scalar and vector quantities.
Work done.
Work done.
Answer
View full question & answer→ Work done-scalar.
Question 681 Mark
Classify the following measures as scalars and vectors.
$10^{-19}$ coulomb
$10^{-19}$ coulomb
Answer
View full question & answer→$10^{-19}$ coulomb is a measure of electric charge and it has magnitude only, therefore, it is a scalar.
Question 691 Mark
Compute the magnitude of the following vectors:
$\vec{a}=\hat{i} + \hat{j}+\hat{k;}$ $ \vec{b}=2\hat{i}-7\hat{j}-3\hat{k};$ $ \vec{c}=\frac{1}{\sqrt{3}}\hat{i}+\frac{1}{\sqrt{3}}\hat{j}-\frac{1}{\sqrt{3}}\hat{k}$
$\vec{a}=\hat{i} + \hat{j}+\hat{k;}$ $ \vec{b}=2\hat{i}-7\hat{j}-3\hat{k};$ $ \vec{c}=\frac{1}{\sqrt{3}}\hat{i}+\frac{1}{\sqrt{3}}\hat{j}-\frac{1}{\sqrt{3}}\hat{k}$
Answer
View full question & answer→The given vectors are:$\vec{a}=\hat{i} + \hat{j}+\hat{k;}$ $ \vec{b}=2\hat{i}-7\hat{j}-3\hat{k};$ $\vec{c}=\frac{1}{\sqrt{3}}\hat{i}+\frac{1}{\sqrt{3}}\hat{j}-\frac{1}{\sqrt{3}}\hat{k};$
$\Big|\vec{a}\Big|=\sqrt{(1)^2+(1)^2+(1)^2}=\sqrt{3}$
$\Big|\vec{b}\Big|=\sqrt{(2)^2+(-7)^2+(-3)^2}$
$=\sqrt{4+49+9}$
$=\sqrt{62}$
$\Big|\vec{c}\Big|=\sqrt{\bigg(\frac{1}{\sqrt{3}}\bigg)^2+\bigg(\frac{1}{\sqrt{3}}\bigg)^2+\bigg(-\frac{1}{\sqrt{3}}\bigg)^2}$
$=\sqrt{\frac{1}{3}+\frac{1}{3}+\frac{1}{3}}=1$
$\Big|\vec{a}\Big|=\sqrt{(1)^2+(1)^2+(1)^2}=\sqrt{3}$
$\Big|\vec{b}\Big|=\sqrt{(2)^2+(-7)^2+(-3)^2}$
$=\sqrt{4+49+9}$
$=\sqrt{62}$
$\Big|\vec{c}\Big|=\sqrt{\bigg(\frac{1}{\sqrt{3}}\bigg)^2+\bigg(\frac{1}{\sqrt{3}}\bigg)^2+\bigg(-\frac{1}{\sqrt{3}}\bigg)^2}$
$=\sqrt{\frac{1}{3}+\frac{1}{3}+\frac{1}{3}}=1$
Question 701 Mark
Classify the following measures as scalars and vectors.
2 meters north-west
2 meters north-west
Answer
View full question & answer→ 2 meters North-West us a measure of velocity. It has magnitude and direction both and hence it is a vector.
Question 711 Mark
In Fig 10.6 (a square), identify the following vectors.
Coinitial.
Coinitial.
Answer
View full question & answer→ $\vec{a}\ \text{and}\ \vec{b}$ have same initial point and therefore coinitial vectors.
Question 721 Mark
Write $\overrightarrow{\text{PQ}}+\overrightarrow{\text{RP}}+\overrightarrow{\text{QR}}$ in the simplified form.
Answer
View full question & answer→ We have, $\overrightarrow{\text{PQ}}+\overrightarrow{\text{RP}}+\overrightarrow{\text{QR}}=\overrightarrow{\text{PQ}}+\overrightarrow{\text{QR}}+\overrightarrow{\text{RP}}$$=\overrightarrow{\text{PR}}+\overrightarrow{\text{RP}}$ $\Big[\therefore\ \overrightarrow{\text{PQ}}+\overrightarrow{\text{QR}}=\overrightarrow{\text{PR}}\Big]$
$=\vec0$
$=\vec0$
Question 731 Mark
Define 'zero vector'.
Answer
View full question & answer→ A vector whose initial and terminal point are coincident is called a zero vector or null vector. The null vector is denoted by $\vec0$. The magnitude of null vectors is zero.
Question 741 Mark
Classify the following as scalar and vector quantities.
Velocity.
Velocity.
Answer
View full question & answer→ Velocity-vector.
Question 751 Mark
Classify the following as scalar and vector quantities:
Displacement.
Displacement.
Answer
View full question & answer→ Displacement is a vector quantity as it involves both magnitude and direction.
Question 761 Mark
Classify the following measures as scalars and vectors.
10 kg.
10 kg.
Answer
View full question & answer→ 10 kg is a measure of mass, it has no direction, it is magnitude only and therefore it is a scalar.
Question 771 Mark
Classify the following as scalar and vector quantities:
Time period.
Time period.
Answer
View full question & answer→ Time period is a scalar quantity as it involves only magnitude.
Question 781 Mark
In Fig 10.6 (a square), identify the following vectors.
Collinear but not equal.
Collinear but not equal.
Answer
View full question & answer→ $\vec{a}\ \text{and}\ \vec{c}$ have parallel support, so that they are collinear. Since they have opposite directions, they are not equal. Hence $\vec{a}\ \text{and}\ \vec{c}$ are collinear but not equal.
Question 791 Mark
Find the direction cosines of the following vector: $2\hat{\text{i}}+2\hat{\text{j}}-\hat{\text{k}}$
Answer
View full question & answer→ We have, $2\hat{\text{i}}+2\hat{\text{j}}-\hat{\text{k}}$ The direction cosines are $\frac{2}{\sqrt{2^2+2^2+(-1)^2}},\frac{2}{\sqrt{2^2+2^2+(-1)^2}},\frac{1}{\sqrt{2^2+2^2+(-1)^2}}$ or, $\frac{2}{3},\frac{2}{3},\frac{-1}{3}$
Question 801 Mark
Classify the following measures as scalar and vector:
45º
45º
Answer
View full question & answer→ 45º is a scalar quantity as it involves only magnitude.
Question 811 Mark
Define unit vector.
Answer
View full question & answer→ A vector whose modulus is unity is called a unit vector. The unit vector in the direction of a vector $\vec{\text{a}}$ is denoted by $\hat{\text{a}}$.
Thus, $|\hat{\text{a}}|=1$
Thus, $|\hat{\text{a}}|=1$
Question 821 Mark
Classify the following as scalar and vector quantities:
Work.
Work.
Answer
View full question & answer→ Work done is a scalar quantity as it involves only magnitude.
Question 831 Mark
Classify the following measures as scalar and vector:
20kg weight.
20kg weight.
Answer
View full question & answer→20kg weight is a vector quantity as it involves both magnitude and direction.
Question 841 Mark
Find the direction cosines of the following vectors:
$3\hat{\text{i}}-4\hat{\text{k}}$
$3\hat{\text{i}}-4\hat{\text{k}}$
Answer
View full question & answer→ We have, $3\hat{\text{i}}-4\hat{\text{k}}$
The direction cosines are $\frac{3}{\sqrt{3^2+0+(-4)^2}},\frac{0}{\sqrt{3^2+0+(-4)^2}},\frac{-4}{\sqrt{3^2+0+(-4)^2}}$ or, $\frac{3}{5},0,\frac{-4}{5}$
The direction cosines are $\frac{3}{\sqrt{3^2+0+(-4)^2}},\frac{0}{\sqrt{3^2+0+(-4)^2}},\frac{-4}{\sqrt{3^2+0+(-4)^2}}$ or, $\frac{3}{5},0,\frac{-4}{5}$
Question 851 Mark
Classify the following as scalar and vector quantities:
Force.
Force.
Answer
View full question & answer→ Force is a vector quantity as it involves both magnitude and direction.
Question 861 Mark
Classify the following measures as scalars and vectors.
$20 m/s^2$
$20 m/s^2$
Answer
View full question & answer→$20 m/sec^2$ is a measure of acceleration. It is a measure of rate of change of velocity, therefore, it is a vector.
Question 871 Mark
Classify the following measures as scalar and vector:
15kg.
15kg.
Answer
View full question & answer→ 15kg is a scalar quantity because it involves only mass.
Question 881 Mark
Show that the vectors $2\hat{i}-3\hat{j}+4\hat{k}\ \text{and}\ -4\hat{i}+6\hat{j}-8\hat{k}$ are collinear.
Answer
View full question & answer→ $\text{Let}\ \vec{a}=2\hat{i}-3\hat{j}+4\hat{k}\ \text{and}\ \vec{b}=-4\hat{i}+6\hat{j}-8\hat{k}.$
It is observed that $ \vec{b}=-4\hat{i}+6\hat{j}-8\hat{k}=-2\Big(2\hat{i}-3\hat{j}+4\hat{k}\Big)=-2\vec{a}$
$\therefore\vec{b}=\lambda\vec{a}$
where,
$\lambda=-2$
Hence, the given vectors are collinear.
It is observed that $ \vec{b}=-4\hat{i}+6\hat{j}-8\hat{k}=-2\Big(2\hat{i}-3\hat{j}+4\hat{k}\Big)=-2\vec{a}$
$\therefore\vec{b}=\lambda\vec{a}$
where,
$\lambda=-2$
Hence, the given vectors are collinear.
Question 891 Mark
Classify the following as scalar and vector quantities.
Force.
Force.
Answer
View full question & answer→Force-vector.
Question 901 Mark
Find the direction cosines of the vector $\hat{i}+2\hat{j}+3\hat{k}.$
Answer
View full question & answer→$\text{Let}\ \vec{a}=\hat{i}+2\hat{j}+3\hat{k}.$
$\therefore\big|\vec{a}\big|=\sqrt{1^2+2^2+3^2}=\sqrt{1+4+9}=\sqrt{14}$
Hence, the direction cosoines of $\vec{a}\ \text{are}\ \bigg(\frac{1}{\sqrt{14}},\frac{2}{\sqrt{14}},\frac{3}{\sqrt{14}}\bigg).$
$\therefore\big|\vec{a}\big|=\sqrt{1^2+2^2+3^2}=\sqrt{1+4+9}=\sqrt{14}$
Hence, the direction cosoines of $\vec{a}\ \text{are}\ \bigg(\frac{1}{\sqrt{14}},\frac{2}{\sqrt{14}},\frac{3}{\sqrt{14}}\bigg).$
Question 911 Mark
Define position vector of a point.
Answer
View full question & answer→A point O is fixed as origin in space (or plane) and P is any point, then $\overrightarrow{\text{OP}}$ is called a position vector of P with reespect to O.
Question 921 Mark
Represent graphically a displacement of 40 km, 30° east of north.
Answer
View full question & answer→Displacement 40 km, 30° East of North $\Rightarrow$ Displacement vector $\overrightarrow{\text{OA}}$ (say) such that $\bigg|\overrightarrow{\text{OA}}\bigg|$ = 40 (given) and vector $\overrightarrow{\text{OA}}$ makes an angle 30° with North in East-North quadrant.
Question 931 Mark
If $\vec{\text{a}}\text{ and }\vec{\text{b}}$ are two non-collinear vectors such that $\text{x}\vec{\text{a}}+\text{y}\vec{\text{b}}=\vec0$, Then write the values of x and y.
Answer
View full question & answer→We have, $\text{x}\vec{\text{a}}+\text{y}\vec{\text{b}}=\vec0$$\Rightarrow\ \text{x}=0$$$ and $\text{y}=0$ $[\because\ \vec{\text{a}}$ and $\vec{\text{b}}$ are non-collinear vectors$]$
Question 941 Mark
In Fig 10.6 (a square), identify the following vectors.
Equal.
Equal.
Answer
View full question & answer→$\vec{b}\ \text{and}\ \vec{d}$ have same direction and same magnitude. Therefore $\vec{b}\ \text{and}\ \vec{d}$ are equal vectors.
Question 951 Mark
Classify the following as scalar and vector quantities.
Distance.
Distance.
Answer
View full question & answer→Distance-scalar.
Question 961 Mark
Classify the following as scalar and vector quantities.
Time period.
Time period.
Answer
View full question & answer→Time-scalar.
Question 971 Mark
Find the direction cosines of the following vector:$6\hat{\text{i}}-2\hat{\text{j}}-3\hat{\text{k}}$
Answer
View full question & answer→We have, $6\hat{\text{i}}-2\hat{\text{j}}-3\hat{\text{k}}$
The direction cosines are $\frac{6}{\sqrt{6^2+(-2)^2+(-3)^2}},\frac{2}{\sqrt{6^2+(-2)^2+(-3)^2}},\frac{-3}{\sqrt{6^2+(-2)^2+(-3)^2}}$ or, $\frac{6}{7},\frac{-2}{7},\frac{-3}{7}$
The direction cosines are $\frac{6}{\sqrt{6^2+(-2)^2+(-3)^2}},\frac{2}{\sqrt{6^2+(-2)^2+(-3)^2}},\frac{-3}{\sqrt{6^2+(-2)^2+(-3)^2}}$ or, $\frac{6}{7},\frac{-2}{7},\frac{-3}{7}$
Question 981 Mark
Classify the following as scalar and vector quantities:
Distance.
Distance.
Answer
View full question & answer→Distance is a scalar quantity as it involves only magnitude.
Question 991 Mark
Classify the following measures as scalars and vectors.
40 watt
40 watt
Answer
View full question & answer→40 Watt is a measure of power. It has no direction, only magnitude and therefore, it is a scalar.
Question 1001 Mark
Classify the following as scalar and vector quantities:
Velocity.
Velocity.
Answer
View full question & answer→Velocity is a vector quantity as it involves both magnitude as well as direction.